# Decimals – Multiplication and Division

These resources offer practice in operating on decimals and, moreover, opportunities to think about the processes of multiplication and division. As stated in the NCTM Focal Points, students should make sense of these procedures, become fluent in performing them, and be able to apply them in solving problems. I believe these sites, as a whole, offer practice in both understanding and problem solving.

Learning about Multiplication Using Dynamic Sketches of an Area Model
In this applet, a rectangle represents the familiar area model of multiplication. By changing the height of the rectangle, students can explore the effect of multiplying a fixed positive number, in this case 3, by decimal numbers greater than 1 and less than 1. The visual is powerful!

Too Big or Too Small?
Scroll down to Activity 3: Exploring the Effect of Operations on Decimals. Through playing the cleverly crafted game presented here, students explore the effect of operations on decimal numbers. They begin with the number 100 as they enter a maze. For each segment chosen on the maze, the student calculates the assigned operation and number; for example, “+ 1.2” or “x 0.8.” The goal is to choose a path through the maze that results in the largest value at the finish.

Decimals
This site has explanatory lessons and interactive practice on most aspects of decimals, including multiplying decimals and dividing them. A good set of materials for self-tutoring or review.

Find the Cost of Meat per Week at a Zoo
In a multi-step, NAEP assessment item, students must determine how much a zoo spends each week on meat to feed the animals. The site links to the scoring guide, sample student responses, and data on how well grade 8 students did on this multiplication/division problem. Only 13% solved it correctly!

Where’s the (Decimal) Point? asks students to explain clearly how they know where to put the decimal point in multiplication and in division of decimals. Students must think beyond the “rules” to the “whys.” I suggest these problems as challenges for older middle school students who are ready to stretch their thinking to the level of generalizing arithmetic.

# Fractions: Multiplying and Dividing

Is there anything more difficult to explain at 5th and 6th grade level than the rules for multiplying and dividing fractions? These resources offer support in explaining the concepts that underlie the rules. Visual, interactive models are provided where possible. You will also find opportunities for your students to practice their skills in this area of arithmetic. If you have other approaches to teaching this topic, please share! Just use the comment box below!

Multiplication of Fractions
Visualize and practice multiplying fractions using an area representation. With the “Show Me” option selected, the virtual manipulative is used to graphically demonstrate, explore, and practice multiplying fractions. A rectangular grid, representing a whole, shows the areas of two fractions to be multiplied, one fraction in red on the left and another in blue at the bottom. The area of the overlapping region, shown in purple, represents the product of their multiplication. The “Test Me” option provides problems to be solved using the same graphical representation.

Multiplying Fractions
This tutorial site offers instruction as well as practice in multiplication of fractions. The fractions are modeled with either circles or lines (rectangular areas). The visual display matched with the numerical makes an effective demonstration.

Divide and Conquer
This lesson is based on the idea that middle school students can better understand the procedure for dividing fractions if they analyze division through a sequence of problems. Students start with division of whole numbers, followed by division of a whole number by a unit fraction, division of a whole number by a non-unit fraction, and finally division of a fraction by a fraction. Activity sheets and guiding questions are included.

Dividing Fractions
In this activity, students divide fractions using area models. They can adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change. Full access to ExploreLearning is available through an annual subscription, but you can apply for a month’s free access in order to test out the applets.

Fraction Bars
This applet offers a classroom-adaptable idea of how to explain division of fractions. Adjustable colored bars are used to illustrate arithmetic operations with fractions on the number line. The initial seeding shows a division problem, dividing 7/5 by ½.